# Logic Problem – Daniel made a spinner – Is it impossible or certain it will always land on a number less than 5?

Subject:

Math

3

Title – Certain or Impossible “less than” Logic Problem Idea
By – Shantal Turner
Primary Subject – Math
Grade Level – 3th

Definitions:

• An event is something that may happen
• An event is certain if it will always happen
• An event is impossible if it will never happen.

Problem:

• Daniel made this spinner for a game.
• Is it impossible or certain that he will spin a number less than 5 on his spinner? =

Solution:

• Ms. Turner did not offer a solution to her problem and only titled it “Certain or Impossible.” How fun! Be sure to find your own solution before looking at what we came up with below, which may not be the intended solution at all!

Possible Solutions (offered by LessonPlansPage.com):

• Whoops:
• Impossible : “This” spinner? What spinner? You can’t actually spin a number on an imaginary spinner.
• Neither : Without knowing what numbers are on the spinner, it is impossible to determine if the event is “certain” or “impossible”. You need to know what number the spinner landed on in order to determine if that number is less than, greater than, or equal to the number 5.
• If you make an actual spinner to show the kids with numbers 1-4 on it:
• Neither: it is not actually certain that he will ever spin the spinner, but if he did…
• Neither: if he spins the spinner, it could actually hit the line.
• Certain : if he spins the spinner and it doesn’t hit the line, it will always hit a number less than 5, because 1, 2, 3, and 4 precede 5 on a number line and stand for a value that is less than 5.
• If you make an actual spinner to show the kids with numbers 5-8 on it:
• Impossible : It will never hit a number less than 5.
• Note: even if it hits a line or he never spins, it still can never hit a number less than 5, because 6, 7, and 8 are greater numbers and stand for greater values than 5.
• If you make an actual spinner to show the kids with numbers 1-6 on it:
• Neither :
• It is not impossible, because it could land on 1, 2, 3, or 4 if he spins an actual spinner with the numbers 1-6 on it.
• It is not certain, because it could land on 5, 6, 7 or 8 which are equal to or greater than 5.
• It is also not certain, because it could land on the line or he could choose to throw away the spinner and never use it.
• If you make an actual spinner to show the kids with all spots labeled with the number 5 on it:
• Impossible : It will never hit a number less than 5, because 5 equals 5, it can never be less than itself.
• Note: even if he never spins or it hits the line, it will still never hit a number less than 5.
• If you make an actual spinner to show the kids with all spots labeled with the number 1 on it:
• Certain : If he spins the spinner and it never hit the line, he will always hit a number less than 5, because 1 is less that 5.

Notes from LessonPlansPage.com:

• This is a great logic problem if your students have a great grasp of number sense and the concepts of less than, greater than, and equal to.
• It would make a great extension for gifted learners.
• If less than, greater than, and equal to is the concept you are trying to teach, be sure to draw an actual spinner on the board and then put on the numbers that you want them think about. Also, be sure to say that the spinner never hits the line (because the line is too thin and the pointer is very big).

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